Josephson tunable metamaterials for quantum devices

目前，人们对量子器件（量子位、探测器等）的发展越来越感兴趣，由于它们的性质，它们可以在低温和超低温下工作，频率为几（几十）GHz。因此，设计在相同温度和频率下工作的功能超材料（滤波器、放大器等），允许控制、处理和读出信息，并放大弱量子信号是非常相关的。超导电性为超材料带来了低损耗、元原子尺寸紧凑等独特优势，而约瑟夫森效应则为原位调整超材料性能提供了可能。在这个联合项目的框架内，我们将在理论上（数值上）和实验上设计、制造和研究几种基于元原子阵列的超材料，如嵌入共面传输线的约瑟夫森结（JJs）或squid。<s:1>宾根研究小组将专注于开发具有独特和可调性能的新型约瑟夫森超材料（jmm）。在线性系统中，我们的目标是设计一个具有可调色散的JMM，例如，它可以作为一个可调的带通或带阻滤波器，或者，例如，具有零群速度的JMM，在那里传播的电磁波可以停止。莫斯科集团的主要关注点更多的是应用导向。这是约瑟夫森行波参数放大器（JTWPA）的开发和实验测试，这是一种在非线性状态下工作的JMM，其中信号频率处的弱输入信号（被放大）与泵频处的强泵信号的非线性混合导致JTWPA输出信号频率处的放大信号。该理论预测，在泵浦频率为12 GHz的情况下，由300个squid组成的JTWPA应在约5 GHz的带宽上提供20 dB的均匀增益。预计在4.2K的温度下，5 GHz的噪声温度将达到0.2 K。在项目的后期阶段，JTWPA将重新设计温度低于1K。t<s:1>宾根研究小组还将通过低温扫描电子（或激光）显微镜（LTSEM/LTSLM）对jmm进行实验研究，这是t<s:1>宾根研究所拥有的一项独特技术。升级后，它将允许可视化jmm（如JTWPA）的操作，并找到问题区域（如果有的话）。在这种情况下，重要的一点是了解(a)单个元原子（对LTSEM/LTSLM成像很重要）或(b)所有元原子（技术扩散）的参数偏差如何影响JMM的操作和性能值。在t<s:1>宾根的研究小组将通过对JMM动力学进行全尺寸非线性数值模拟来研究这个问题。最后，由<s:1>宾根小组设计的新型jmm将在莫斯科制造，并由两个小组进行实验研究。

Presently there is a growing interest in development of quantum devices (qubits, detectors, etc.) that, due to their nature, operate at low and ultra low temperatures and at frequencies of several (tens of) GHz. Therefore, the design of functional metamaterials (filters, amplifies, and so on) that operate at the same temperatures and frequencies and allow to control, process and readout of the information as well as amplify weak quantum signals is very relevant. Superconductivity brings unique advantages to metamaterials such as low loss, compact dimensions of meta-atoms, while the Josephson effect provides the possibility to tune metamaterial properties in-situ.In the framework of this joint project we are going to design, fabricate and investigate both theoretically (numerically) and experimentally several metamaterials based on arrays of meta-atoms, such as Josephson junctions (JJs) or SQUIDs, embedded into coplanar transmission line. The Tübingen group will focus on the development of novel Josephson MetaMaterials (JMMs) with unique and tunable properties. In the linear regime the aim is to design a JMM with the tunable dispersion that allows to create, \eg, JMM that works as a tunable band-pass or band-rejection filter or, \eg, JMMs with zero group velocity, where the propagating electromagnetic waves can be stopped.The main focus of the Moscow group is more application oriented. It is the development and experimental tests of the Josephson Traveling Wave Parametric Amplifier (JTWPA) --- a JMM working in a non-linear regime, where non-linear mixing of a weak input signal (to be amplified) at the signal frequency with the strong pump signal at pump frequency results in an amplified signal at the signal frequency at the output of the JTWPA. The theory predicts that a JTWPA consisting of 300 SQUIDs should provide a uniform gain of 20 dB over the bandwidth of about 5 GHz at the pump frequency of 12 GHz. The noise temperature is expected to reach 0.2 K at 5 GHz at a temperature of 4.2K. At the later stage of the project the JTWPA will be redesigned for temperatures below 1K.The Tübingen group will also investigate JMMs experimentally by means of Low Temperature Scanning Electron (or Laser) Microscopy (LTSEM/LTSLM) -- a unique technique available in Tübingen. After upgrade, it will allow to visualize the operation of the JMMs such as JTWPA and find the problem areas if any. In this context an important point is to understand how the deviation of parameters of (a) one single meta-atom (important for LTSEM/LTSLM imaging) or (b) all meta-atoms (technological spread) affect the operation and figures of merit of JMM. The group in Tübingen will investigate this question by making full scale non-linear numerical simulations of JMM dynamics.Finally, novel JMMs designed by the Tübingen group will be fabricated in Moscow and experimentally investigated by both groups.